OR Prove that \( y \frac{d y}{d x}+x=0 \) if \( x=\frac{1-t^{2}}{1+t^{2}} \quad y=\frac{2 t}{1+t^{2}} \) Determine whether the given function ?

Discur the convergene at \( [1,2] \) given that \( f(x)=x^{3}-x-1 \)

Find the area of the region bounded by the curves \( y = \frac{1}{x} \) from \( x = 1 \) to \( x = 2 \) and the line \( y = 1 \).

30. \( \int_{0}^{1} \sqrt{x-x^{2}} d x \)

\( \int _{}^{}\frac{\sqrt {x}}{\sqrt [3]{x}+1} d \)

CQALCULEN LeN Limi te SuiU \( \lim _{x \rightarrow 3} \frac{3}{x-3} ; \) \( \lim _{x \rightarrow 3} \frac{x^{2}-9}{x-3} \) \( \lim _{x \rightarrow 1} \frac{x+1}{x-1} \) \( \lim _{x \rightarrow-2} \frac{x^{2}-3 x+1}{x+2} \) \( \lim _{x \rightarrow 1} \frac{-x-2}{x^{2}-4 x+3} \)